Which is greater: `(3)/(11)` of `(2)/(5)` or `(4)/(7)` of `(5)/(8)` ?

Answer

To determine which is greater between \(\frac{3}{11} \times \frac{2}{5}\) and \(\frac{4}{7} \times \frac{5}{8}\), we will follow these steps:

### Step 1: Calculate \(\frac{3}{11} \times \frac{2}{5}\)
To multiply two fractions, we multiply the numerators together and the denominators together.

\[ \frac{3}{11} \times \frac{2}{5} = \frac{3 \times 2}{11 \times 5} = \frac{6}{55} \]

### Step 2: Calculate \(\frac{4}{7} \times \frac{5}{8}\)
Similarly, we multiply the numerators and the denominators.

\[ \frac{4}{7} \times \frac{5}{8} = \frac{4 \times 5}{7 \times 8} = \frac{20}{56} \]

### Step 3: Simplify \(\frac{20}{56}\)
Next, we simplify \(\frac{20}{56}\) by finding the greatest common divisor (GCD) of 20 and 56, which is 4.

\[ \frac{20 \div 4}{56 \div 4} = \frac{5}{14} \]

### Step 4: Compare \(\frac{6}{55}\) and \(\frac{5}{14}\)
To compare these two fractions, we can cross-multiply:

- Cross-multiply \(\frac{6}{55}\) and \(\frac{5}{14}\):

\[ 6 \times 14 = 84 \]
\[ 5 \times 55 = 275 \]

### Step 5: Determine which is greater
Now we compare the results of the cross-multiplication:

\[ 84 < 275 \]

This means:

\[ \frac{6}{55} < \frac{5}{14} \]

### Conclusion
Thus, \(\frac{5}{14}\) is greater than \(\frac{6}{55}\), which means:

\[ \frac{4}{7} \times \frac{5}{8} > \frac{3}{11} \times \frac{2}{5} \]

### Final Answer
\(\frac{4}{7} \times \frac{5}{8}\) is greater than \(\frac{3}{11} \times \frac{2}{5}\).

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